Elastic Wave Scattering By A Canyon Or Tunnel In Layered Saturated Half Space

The analysis of wave propagation in layered saturated soil is important both in theory and engineering. Wolf derived dynamic-stiffness matrix of elastic layered soil, which formed a complete theory for wave propagation in layered site and dynamic soil-structure interaction. How to extend Wolf's theory to the case of poroelasticity will be mainly resolved in this paper.According to the practical Biot's equation, general solutions of the wave equations are deduced by introducing wave potentials. Then exact and symmetric dynamic-stiffness matrices of a layered saturated soil and half-space are derived. All parameters have explicitly physical meaning and the thickness of sub-layers has no influence on the calculation precision, which is very convenient to engineering application. Based on these matrices, Green's functions are derived for distributed loads or pore pressure acting on inclined line in a layered poroelastic site, which resolved the key problems in wave scattering by local soil conditions and dynamic soil-structure interaction by using the indirect boundary element method (IBEM).Free-filed response of layered saturated site is systematically researched. Free-surface motion of half-space caused by incident wave is discussed in drained or undrained boundary condition. Two typical layered saturated sites: single layer on half-pace and increasing stiffness site are analyzed.Scattering of plane elastic waves by a canyon in layered saturated site is analyzed by IBEM. Shear modulus, porosity and permeability of saturated soil and different boundary permeability conditions have an significant influence on the wave scattering. The amplitudes of displacements depend on the thickness and rigidity of covering soil greatly, which shows the necessity to use the layered model.The differences of amplification of elastic waves by a cavity in single-phase layered and in homogeneous half-space are studied by using the IBEM. The reasons for these differences are also discussed. The necessity and rationality of using layered model are pointed. Scattering of elastic waves by a cavity in a layered saturated site is analyzed by IBEM. The drainage condition at the interface and the frequency of incident waves have an important influence on the amplitudes of surface displacements. As a whole, the surface displacements in the case of undrained condition are larger than the corresponding displacements in the case of drained condition. The wave scattering by a cavity in a layered saturated site is quite different from the wave scattering by a cavity in a layered dry site. It is shown that porous fluid plays an important role in dynamic response of layered poroelastic site. This method can be used in the dynamic analysis of underground structures such as cavity.